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Abstract

We introduce theoretically and demonstrate experimentally a contrast transfer function based phase retrieval algorithm that reconstructs the projected thickness of an homogeneous sample using a polychromatic x-ray source. We show excellent quantitative recovery of test samples in 2D using a synchrotron source with significant harmonic contamination, and in 3D using a laboratory source.

a) 2D Diffraction pattern of a hollow polyimide tube with an outer diameter of 168 µm and an inner diameter of 122 µm; b) 2D reconstructed thickness using Eq. (14); c) profiles of the reconstructed thickness across the white dashed line shown in (b) for different approaches described in the text. There was a small feature on the wall the tube; it can be seen as a small region in the middle of the tube in both the diffraction pattern (a) and in the reconstruction (b). The polychromatic CTF is not only able to reconstruct the correct projected thickness but also be able to reconstruct a small feature on the wall of the tube.